In this section we show by means of the example below that when two vector fields have a.e. vanishing Lie bracket, it is in general not true that their flows commute a.e. even if we assume that they are a.e. uniquely defined, and even if they are regular Lagrangian. The main idea comes from an example [1]} of non-commutativity of groups with generators commuting on a common dense set. In our case, we consider a foliation of \(\mathbb {R}^d\)  into helix-like hypersurfaces so that the composition of the two flows yields a rotation along the axis of the helix.
